Problem: Simplify the following expression: $\sqrt{40}+\sqrt{160}+\sqrt{250}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{40}+\sqrt{160}+\sqrt{250}$ $= \sqrt{4 \cdot 10}+\sqrt{16 \cdot 10}+\sqrt{25 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{10}+\sqrt{16} \cdot \sqrt{10}+\sqrt{25} \cdot \sqrt{10}$ $= 2\sqrt{10}+4\sqrt{10}+5\sqrt{10}$ Finally, simplify by combining the terms. $= ( 2 + 4 + 5 )\sqrt{10} = 11\sqrt{10}$